Roughly chop mushrooms.
Add oil and butter to a large, heavy pot and cook over medium-high until butter melts.
Add mushrooms, salt, and pepper; cook, stirring often, until mushrooms are deeply browned and most of the moisture has evaporated, 8 to 10 minutes.
Add shallots and scallions; cook, stirring often, until softened, about 4 minutes.
Add flour and stir to combine.
Add stock and milk, stirring and scraping to loosen any browned bits from bottom of pot. Let mixture come to a low boil and cook, stirring occasionally, until broth thickens, about 5 minutes. Remove from heat.
Transfer half of mixture to a countertop blender. Secure lid on blender and remove center piece to allow steam to escape. Place a clean towel over opening and process until almost smooth; return to pot. Or use an immersion blender to pulse the soup until somewhat blended but some whole pieces of mushroom are still visible.
Stir in parsley and tarragon; serve hot.
